[3] Neokosmidis Techniques for FWM Suppresion
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New Techniques for the Suppression of the Four
Wave Mixing-Induced Distortion in Non-Zero
Dispersion Fiber WDM Systems
I . Neokosmidis, T. Kamalakis, A. Chipouras and T. Sphicopoulos
Department of Informatics and Telecommunications, University of Athens
Panepistimiopolis Ilissia, Athens, Greece, GR-15784
i.neokosmidis@di.uoa.gr
Abstract: The performance of a Wavelength Division Multiplexing (WDM) optical
network can be severely degraded due to fiber nonlinear effects. In the case where
Non-Zero Dispersion (NZD) fibers are employed, the Four Wave Mixing (FWM)
effect sets an upper limit on the input power especially in the case of narrow channel
spacing. In order to reduce FWM-induced distortion two new techniques, the hybrid
ASK/FSK modulation and the use of pre-chirped pulses, are investigated. It is shown
that both techniques can greatly improve the Q factor in a 10Gb/s WDM system. This
happens even for very high input powers (~10dBm) where the degradation of the
conventional WDM system is prohibitively strong. The proposed methods are also
applied and tested in higher bit rates (40Gbps). It is deduced that although the hybrid
ASK/FSK modulation technique marginally improves the system performance, the
optical pre-chirp technique can still be used to greatly increase the maximum
allowable input power of the system.
Index Terms: Chirp, nonlinear optics, optical crosstalk, optical fiber
communications, wavelength division multiplexing.
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I. INTRODUCTION
Wavelength Division Multiplexing (WDM) is widely being adopted as a
means to increase the capacity of optical networks. However, the rapid growth in the
number of Internet users and the need for provision of new broadband services is
expected to significantly increase the traffic volume. There is thus a tendency to
develop larger WDM networks with narrower channel spacing and higher channel
capacity. Furthermore, a significant decrease of the overall cost can be accomplished
by reducing the number of optical amplifiers used in the links which leading to the
use of higher input power at the transmitter. However, this increase in the optical
power results to signal degradation due to fiber nonlinear effects, including Four
Wave Mixing (FWM), Cross Phase Modulation (XPM) and Self Phase Modulation
(SPM).
Both XPM and FWM introduce intensity fluctuations that are dependent on
the neighboring channels, resulting into interchannel interference throughout the fiber
length. SPM is generally considered negligible compared to XPM, since even for a
system of two optical channels XPM is twice as effective as SPM for the same
intensity [1, p. 262]. However, in WDM systems employing Non-zero Dispersion
(NZD) fibers the main nonlinear induced penalty arises from FWM. This is especially
true in systems with dispersion compensation in which the XPM induced distortion is
diminished [2]-[3].
In recent years, several FWM suppression techniques have been proposed.
Since the power of the FWM products decreases quickly as the fiber dispersion
increases, one solution is to use standard single mode fibers. This however, results in
a large dispersion accumulation at the receiver and necessitates the use of long
dispersion compensating fibers in each network node. Another approach is to use
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optical multiplexers and demultiplexers with the combination of delay lines [4], bit-
phase arranged RZ (BARZ) signals [5], hybrid WDM/TDM technique [6],
polarization-division multiplexing [7] and unequal channel spacing [8]-[10]. The
above techniques come at the expense of less channel efficiency or / and more
network complexity. For example, the use of unequal channel spacing requires the
design of optical multiplexers and demultiplexers with central wavelengths not
compatible with the ITU grid.
In this paper, two new methods based on a hybrid ASK/FSK modulation and
pulse pre-chirping are proposed for the suppression of the FWM effect. The basic
ideas behind these methods are summarized as follows. FWM is a nonlinear process
in which three waves of frequenciesfi,fj andfk(ki, j) interact through the third-order
electric susceptibility of the optical fiber to generate a product wave at frequency
fijk=fi+fj-fk. In a WDM system, a product is generated for every possible combination
of channels. Therefore, even if the system has only ten channels, hundreds of new
components are generated. If the channels are assumed to be in-phase and equally
spaced then the efficiency of the FWM process is high and most of the generated
components will be located at the channel frequencies. By FSK modulating the WDM
channels, the spectral position of the FWM components is altered and hence less
products fall near the central frequency of the WDM channels. Hence the
accumulation of the FWM noise is reduced. On the other hand the optical pre-chirping
increases the phase mismatch by randomizing the phases of the input signals. Since
the efficiency of the FWM process is inversely proportional to the phase mismatch it
follows that optical pre-chirping can suppress the FWM noise.
The effectiveness of the new methods is studied by numerically solving the
basic nonlinear propagation equation with the Split Step Fourier Method (SSFM) [1].
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Simulations show that both techniques can provide a significant improvement on the
Q factor obtained at the receiver. The maximum allowable input power is
significantly increased and a power gain that can be as high as 3dB may be obtained
for 10Gb/s WDM systems. The effectiveness of the two techniques is also tested for
higher transmission rates. It is shown that the hybrid ASK/FSK modulation can only
marginally improve the performance of a 40Gb/s WDM system. Optical pre-chirping
on the other hand, offers a significant improvement even for these high bit rates.
The paper is organized as follows: The system configuration is shown in
section II. The transmission model used to study the system under consideration is
described in section III. In section IV, the importance of the FWM-induced distortion
in a conventional WDM system is discussed. The basic concepts of the proposed
compensation techniques are illustrated in section V. The results obtained by the
application of the two methods are presented and discussed in section VI. Some
concluding remarks are given in section VII.
I I . SYSTEM CONFIGURATION
A conventional WDM link is shown in figure 1. The WDM channel are ASK
modulated and multiplexed in a single WDM signal. The WDM signal is then
launched into a Non-Zero Dispersion Fiber. As the signal propagates through the
fiber, nonlinear effects can cause interchannel interference and degrade its quality. At
the receiver the signals are dispersion compensated and demultiplexed. Each signal is
then detected using a direct detection receiver. The receiver may consist of a
photodiode, an electrical amplifier and an electrical filter. After the filter the signal is
sampled and a decision threshold device is used to detect whether a 1 or a 0 is
received.
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In this paper, the input optical power waveform representing a single 1-bit,
p1(t) is specified within the time interval [0, (1+b)Tp] as [11]:
[ ] [ ]{ }[ ]
+
+=
ppin
ppp
pp
pin
TTbtP
TbTandTbt
TT
btTbPtp
,,
)1(,,0,22)1(sin1)(1
(1)
wherePin denotes the peak input power, Tp represents the bit duration and b specifies
the pulse shape. Varying b from 1 to 0, the pulse changes from cos2(t)-like to
rectangular. To estimate the performance of the system, the input channels will be
assumed modulated by a 28
-1 pseudorandom bit streams of the above shape.
Throughout this work NRZ pulses are used with a value ofb=0.4. Finally, the bit
duration Tp was taken to be 100ps for bit rateR=10Gbps and Tp=25ps forR=40Gbps.
The central channel of the WDM system is assumed to be located around 0=1.55m.
The NZD transmission fiber is assumed to have a chromatic dispersion
coefficient D=2ps/nm/km, an optical loss coefficient adB=0.2dB/Km and a nonlinear
coefficient =2(Watt x km)-1. The Dispersion Compensating Fiber (DCF) used at the
receiver has D=-200ps/nm/km, adB=0.5dB/km and =4.5(Watt x km)-1. The total
length of the optical link is L=160Km. At its ith output port, the WDM demultiplexer
is assumed to have a Gaussian transfer function,
( )( )
2
2
2 c
i
f
ff
i efH
= (2)
where
)10ln(2
Bfc
= (3)
In the above equations, B is the 40dB bandwidth of the demultiplexer and fi is the
central frequency of each channel. The Gaussian transfer function is often
encountered in many practical demultiplexers (i.e. Arrayed Waveguide Gratings [12]).
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I I I. THE TRANSMISSION MODEL
In order to test the performance of the system, the fibers propagation equation
can be numerically solved using the Split Step Fourier Method (SSFM) [1, pp. 51-53].
The basic propagation equation is written as:
AAjAt
Aj
z
A 22
2
222
+
=
(4)
where A=A(t,z) is the slowly varying complex envelope of the optical field at time t
and positionzalong the fiber, 2 is the Group Velocity Dispersion (GVD) parameter,
=adB/4.343 is the fiber loss coefficient and is the nonlinear coefficient of the fiber.
In a WDM system consisting ofN channels, the input signal (z=0) can be
written as:
=
=N
i
tfj
iietAtA
1
2)0,()0,(
(5)
whereAi(t,0) and fi are the slowly varying envelope and the central frequency of the
i-th channel respectively. Equation (4) under the initial condition (5) can be used to
describe the signal propagation taking into account the optical losses, chromatic
dispersion and the three Kerr-induced nonlinear phenomena namely the SPM, XPM
and FWM effects.
All channels are assumed aligned in time at the input (synchronous WDM
system) and equally spaced. Under these conditions the strength of FWM effect is
maximized. In order to investigate the performance of a WDM system, the Q factor
can be calculated from the eye diagrams at the receiver. The Q factor is a commonly
used parameter in telecommunications and it is expressed as:
o
oPPQ
+
=
1
1 (6)
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where and are the average optical power of bits 1 and 0 respectively
and 1 and o are the corresponding standard deviations of the noise.
IV. IMPORTANCE OF THE FWM INDUCED DISTORTION
As WDM channels become denser, the power limitations imposed by
nonlinear effects, become more pronounced. FWM introduces intensity fluctuations in
a WDM channel due to the existence of the other channels. The power of these
fluctuations increases with decreasing channel spacing and causes interchannel
interference at the receiver.
Before discussing the FWM compensation techniques, it will be useful to
compare the FWM contribution to system degradation with that induced by XPM and
SPM effects. In order to accomplish this comparison, the effect of SPM and XPM can
be isolated from the effect of FWM by numerically solving the set of coupled
propagation equations (7)
i
il
liii
ii
ii AAAjA
a
t
Aj
t
A
z
A
+=+
+
+
22
2
2
21 222
(7)
instead of equation (4), where Ni 1 andAi=Ai(t,z) is the envelope of the i channel
as above. Also 1i is the inverse of the group velocity at the frequency fi and 2i is the
GVD parameter at the same frequency. Note that in the above system of equations the
SPM effect is described by the j|Ai|2 on the right hand side of (7) while the XPM
effect is described by the sum 2jAili|Al|2. Since the FWM is not taken into account
in (7), a comparison between the solutions of (4) and (7) can be used to estimate the
importance of the FWM-induced distortion in the WDM link.
In order to ascertain that the FWM is indeed the dominant noise source, the
eye diagrams of the central channel are plotted in figure 2, in the case where a) Only
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SPM is assumed (i.e. only the central WDM channel is on), b) only SPM and XPM
are assumed, c) FWM, XPM and SPM are assumed. An 8 channel 10Gb/s WDM
system is assumed with a channel spacing of 50GHz. As seen by the eye diagrams of
figure 2, the degradation induced by SPM and XPM is much lower than that of FWM
and hence, in a WDM link with NZDF, the FWM imposes the severest limitations.
The results of figure 2 can also be justified theoretically. In [13], it is shown
that the XPM intensity fluctuations depend on the accumulated dispersion of the span.
When dispersion compensation is used, the XPM-induced intensity distortion is
greatly diminished. On the other hand the FWM-induced intensity distortion rests
almost unaffected from dispersion compensation. Also as shown in [13] the FWM-
induced intensity distortion decreases as 1/2 and as 1/|2|, while the XPM distortion
decreases much slower. It is therefore not surprising that in the dense WDM system
considered, the FWM-induced intensity distortion dominates over the XPM effect.
V. DESCRIPTION OF THE FWM COMPENSATION SCHEMES
A. Hybrid FSK/ASK Modulation Technique
In order to explain the effectiveness of the hybrid ASK/FSK technique, we
first consider 3 CW waves at frequencies f1, f2 and f3. The FWM products, will be
located at frequenciesfpqr=fp+fq-fr, wherep,q,rtake the values 1,2 or 3.As mentioned
in the introduction, if the channels are equally spaced, the central frequency of the
products will coincide with some of the central frequencies of the channels. In order
to reduce the number of FWM products that coincide with the WDM channels, one
solution is to modulate the WDM signals using a special kind of FSK modulation. In
the context of this special scheme, the WDM channels are divided into pairs and on
each pair the channels follow the same FSK modulation. The FSK modulation of two
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adjacent pairs is opposite, i.e. if the channels in a pair are detuned + away from their
central frequency, the channels of the adjacent pair are inversely detuned and so
on as shown in figure 3. Note that a similar (but constant) channel detuning scheme is
also used in the unequal channel spacing technique [10]. The hybrid ASK/FSK
system structure is depicted in figure 4a.
Figure 4b, depicts the optical spectrum of a hybrid ASK/FSK signal with a
10Gb/s ASK rate and a 1Gb/s FSK rate. The peak optical power of the ASK signal is
Pin=10dBm and a =5GHz detuning. The modulation of the FSK signal is 1,0,1,0,
,0,1. From figure 4b one can notice the two peaks caused by the FSK modulation.
B. Optical Pre-chirp
In this section optical pre-chirping is proposed as another solution for the
reduction of the effect of the FWM induced distortion. Since the efficiency of the
FWM products are inversely proportional to the phase mismatch, it follows that
reducing the phase coherence may reduce the power of the FWM noise. One way to
reduce this coherence is through pulse pre-chirping. Note that a similar technique is
used in the suppression of the XPM induced distortion in systems employing standard
fibers [14]-[15]. In the case of NZD fibers, where the FWM effect dominates as
discussed in section IV, optical pre-chirping will be shown to greatly improve the Q
factor by suppressing the FWM effect.
There are several methods to produce a pre-chirped signal such as cascading
intensity and phase modulators or using dispersion-compensating devices like chirped
fiber gratings and DCFs. In this work, the latter technique was chosen due to its ease
of implementation. The optimal length of the DCF fiber used at the transmitter, in
order to pre-chirp the optical pulses was evaluated through iterative simulations that
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aimed to maximize the performance of the system. The system configuration is shown
in figure 5. Note a DCF is also used at the receiver in order to compensate the
remaining accumulated dispersion of the signal. In this configuration, Pin designates
the power at the end of the transmitter DCF.
VI . EFFECTIVENESS OF THE PROPOSED METHODS
In order to investigate the performance improvement of the two techniques, a
series of simulations were performed using the SSFM method. The 40dB bandwidth
B of the optical demultiplexer was optimized at the receiver in order to achieve the
highest Q factor value for the different values of the input powerPin.
In figure 6, the eye diagrams for the 5th channel (central channel) of a single
span eight-channel WDM system in the case when a) none of the two methods is
applied (conventional WDM system), b) the hybrid ASK/FSK modulation is applied
and c) when the pre-chirped pulses are used. A 10Gb/s WDM system is assumed with
channel spacing equal to 50GHz. The channel detuning of the hybrid ASK/FSK
system is =5GHz and the FSK modulation rate is 1Gb/s. A 225m DCF fiber was
used for optical pre-chirping, with parameters as given in section II. This figure
provides a first indication of the performance improvement of the two techniques. As
shown in the figure, the eye-diagram of the uncompensated system is closed due to
the effect of the FWM induced distortion. The Q factor in this case is 3.4 resulting in
a high error probability. If the FWM is assumed to follow Gaussian distribution, this
Q factor corresponds to an error probability of erfc(Q/ 2 )/23x10-4. However,
adopting the hybrid ASK/FSK modulation technique, the quality of the link is
significantly improved as shown by the second eye-diagram. The Q factor in this case
is 7.5, implying an error probability of the order 10-14. The results are even better for
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the case of optical pre-chirping in which case the Q factor is 10.8 and the
corresponding error probability is even lower. Hence, the effectiveness of the
proposed methods on reducing the FWM noise is clearly seen even for input powers
as high as ~10dBm where the degradation of the conventional WDM system is
prohibitively high.
To further illustrate the effectiveness of the proposed methods and gain a more
quantitative aspect at the performance of each compensation scheme, the Q factor was
evaluated for various values of the input power. Figure 7 depicts the Q factor of the
central channel (worst case) as a function of the input powerPin assuming a 10Gb/s
WDM system with a) N=8 channels and a channel spacing fch=50GHz, b) N=8
channels and a fch=100GHz, c) N=16 channels and fch=50GHz and d) N=16
channels and a fch=100GHz spacing. The FSK modulation rate for the hybrid
ASK/FSK is 1Gb/s and a =5GHz frequency detuning is used. The DCF fiber used in
the above cases is 225m, 150m, 48.5m and 19.4m for figures 7(a), 7(b), 7(c) and 7(d)
respectively. As shown by the figures, both techniques greatly improve the Q factor in
all cases. For example, in the case of a N=16 WDM channel system with 100GHz
channel spacing (figure 7d), the obtained Q factor forPin=14dBm was approximately
5.3 for the uncompensated system and 8.8 for the hybrid ASK/FSK modulation at the
transmitter. These values correspond to a Q factor improvement of 2.2dB. It can also
be seen that while a Q factorQ=10 is achieved forPin=12.3dBm for the conventional
system, the same Q factor value is achieved forPin=13.8dBm in the case of the hybrid
ASK/FSK modulation technique. This corresponds to a power gain of 1.5dB.
The results obtained from the optical pre-chirping technique are even better. In
this case the Q factor is Q=15.1 forPin=14dBm. It is understood that the improvement
of the Q factor is 4.55dB. In order to obtain Q factor equal to 10 the input power can
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be as high as 15dBm, and this translates to a power gain greater than 2.5dB. Note that
this power gain of 2.5dB can be used to increase the tolerance of the system or
increase the span length by 2.5/0.2=12.5Km. Similar results can also be observed for
the other cases considered in the figure. It is therefore evident that both techniques
offer a significant improvement in the performance of the system.
In all cases the Q factor is reduced as the input power increases. This is not
surprising, since it is well known that the power of the produced components is
proportional to Pin3. Hence, these results demonstrate again the strong dependence of
the FWM noise and consequently of the Q factor on the input power. However, the
improvement of the proposed techniques is significant even for high input powers.
In figure 8, the performance improvement of the two techniques in the case of
a 8 channel 40Gb/s WDM system is investigated. The channels are assumed to have
200GHz spacing while the rest of the parameters are the same as those of the 10Gb/s
WDM system considered earlier. The FSK modulation rate for the hybrid ASK/FSK
is 1Gb/s and a =5GHz frequency detuning is used. The DCF fiber used in the above
case is 193.9m. The hybrid ASK/FSK modulation technique only marginally
improves the system performance. On the other hand the use of optical pre-chirped
pulses significantly improves the value of the Q factor. ForPin=14dBm the Q factors
of the conventional and the prechirped system is approximately equal to 8.0 and 16.0
implying a 3dB improvement. Also a power gain as high as 2.5dB is obtained for
Q=12.
It seems therefore that pre-chirping the optical channels can be used in order
to reduce the FWM-induced distortion for a 40Gb/s WDM system as well. Although
40Gb/s WDM systems are presently not used in commercial networks, they may
constitute an option for future all-optical backbone networks. It should also be noticed
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that the optical pre-chirping can be implemented with greater ease than the hybrid
ASK/FSK modulation technique. A single DCF at the receiver can be used to
simultaneously pre-chirp all the WDM signals. On the other hand, the hybrid
ASK/FSK technique may prove more amenable for integration with the WDM
multiplexer on a single chip.
In addition, both methods seem to present significant advantages compared to
other suppression techniques since they overcome some problems. For example, the
use of unequally channel spacing [8]-[10] comes at the expense of increased
multiplexer / demultiplexer design complexity. In [10] the BER is improved by one
order of magnitude while, as shown in this section, the proposed techniques achieve
many orders of magnitude improvement. Unlike the hybrid TDM/WDM technique
[6], these methods do not require the allocation of time slots and the generation of RZ
pulses. The optical delay line technique [4] is applicable only when zero dispersion
fibers are used. It is also interesting to note that the methods proposed in this paper
employ NRZ modulation which is more easily implemented than the RZ modulation.
VII. CONCLUSIONS
In this paper, two techniques, hybrid ASK/FSK modulation and pre-chirping
the optical pulses, are applied to suppress the FWM-induced distortion which can
pose important limitation on the input power of a WDM system. The effectiveness of
the two methods is numerically demonstrated using the Split Step Fourier Method
(SSFM) to simulate the WDM signal propagation. From the obtained results, it is
shown that both techniques greatly improve the performance of the system, providing
a power gain that can be as high as 2.5dB in the case of a 10Gbps WDM system. Pre-
chirping the optical pulses can also be used for the reduction of the FWM-induced
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distortion for a higher bit rate (40Gb/s) system as well and seems to be more easily
implemented than the hybrid ASK/FSK modulation technique.
REFERENCES
[1] G. P. Agrawal,Nonlinear Fiber Optics, 2nd ed. New York: Academic, 1995.
[2] A. V. T. Cartaxo, Cross-Phase Modulation in Intensity Modulation- Direct
Detection WDM Systems with Multiple Optical Amplifiers and Dispersion
Compensators, J. Lightwave Technol., vol. 17, No. 2, pp. 178-190, February 1999.
[3] R. Hui, K. R. Demarest and C. T. Allen, Cross-Phase Modulation in Multispan
WDM Optical Fiber Systems, J. Lightwave Technol., vol. 17, No. 6, pp. 1018-1026,
June 1999.
[4] K. Inoue, Suppression Technique for Fiber Four-Wave Mixing Using Optical
Multi-/Demultiplexers and a Delay Line, J. Lightwave Technol., vol. 11, No. 3, pp.
455-461, March 1993.
[5] K. Sekine, N. Kikuchi, S. Sasaki and H. Ikeda, FWM crosstalk reduction using
bit-phase arranged RZ (BARZ) signals in WDM systems, in Proc. Optoelectronics
and Communications Conf. (OECC) 96, 1996, pp. 114-115, paper 17B2-4.
[6] A. Okada, V. Curri, S. M. Gemelos and L. G. Kazovsky, Reduction of Four-
Wave Mixing crosstalk using a novel hybrid WDM/TDM technique, ECOC98,
1998, pp. 289-290.
[7] K. Sekine, S. Sasaki and N. Kikuchi, 10Gbit/s four-channel wavelength- and
polarization-division multiplexing transmission over 340km with 0.5nm channel
spacing, Electron. Lett., vol. 31, pp. 49-50, 1995.
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[8] F. Forghieri, R. Tkach, A. Chraplyvy and D. Marcuse, Reduction of four-wave
mixing crosstalk in WDM systems using unequally spaced channels, IEEE Photon.
Technol. Lett., vol. 6, pp. 754-756, 1994.
[9] H. Suzuki, S. Ohteru and N. Takachio, 22 x 10 Gb/s WDM transmission based on
extended method of unequally channel allocation around the zero-dispersion
wavelength region, IEEE Photon. Technol. Lett., vol. 11, pp. 1677-1679, 1999.
[10] A. Boskovic, S. Ten and V. L. da Silva, FWM penalty reduction in dense WDM
systems through channel detuning, ECOC98, 1998, pp. 163-164.
[11] P. J. Winzer, M. Pfennigbauer, M. M. Strasser and W. R. Leeb, Optimum Filter
Bandwidths for Optically Preamplified NRZ Recievers, J. Lightwave Technol., vol.
19, No. 9, pp. 1263-1273, September 2001.
[12] M. K. Smit and C. Dam, PHASAR-Based WDM-Devices: Principles and
Applications,IEEE J. Selected Topics in Quant. Elec. Vol. 2, No. 2, June 1996, pp.
236-250.
[13] B. Xu and M. Brandt-Pearce, Comparison of FWM- and XPM-Induced
Crosstalk Using the Volterra Series Transfer Function Method, J. Lightwave
Technol., vol. 21, No. 1, pp. 40-53, January 2003.
[14] A.Sano, Y. Miyamoto, S. kuwahara and H. Toba, A 40Gb/s/ch WDM
transmission with SPM/XPM suppression through prechirping and dispersion
management, J. Lightwave Technol., vol. 18, pp. 1519-1527, 2000.
[15] A. Sano and Y. Miyamoto, Performance evaluation of prechirped RZ and CS-
RZ formats in high-speed transmission systems with dispersion management, J.
Lightwave Technol., vol. 19, No. 12, pp. 1864-1871, December 2001.
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Figure 1
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Figure 2
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Figure 3
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Figure 4
(a)
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Figure 6
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5 6 7 8 9 100
4
8
12
16
20
2428
32
36
40
44
(a)
Qf
actor
Pin(dBm)
Uncompensated system
With FSK
With pre-chirp
5th channel
10 11 12 13 14 154
8
12
16
20
24
28
32
36
40
(b)
Qf
actor
Pin(dBm)
Uncompensated system
With FSK
With pre-chirp
5th channel
4 5 6 7 8 94
8
12
16
20
24
28
32
36
40
(c)
Qf
actor
Pin(dBm)
Uncompensated system
With FSK
With pre-chirp
8th channel
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10 11 12 13 14 154
8
12
16
20
2428
32
36
40
(d)
Qf
actor
Pin(dBm)
Uncompensated system
With FSK
With pre-chirp
8th channel
Figure 7
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24
10 11 12 13 14 154
8
12
16
20
24
28
32
36
Qf
actor
Pin(dBm)
Uncompensated system
With FSK
With pre-chirp
5th channel
Figure 8
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25
Figure Captions
Fig. 1: System structure.
Fig. 2: Comparison of the SPM, XPM and FWM effect when Pin=10dBm. a) SPM
effect, b) SPM and XPM effects, c) SPM, XPM and FWM effects
Fig. 3: The FSK modulation scheme used in the proposed system
Fig. 4: a) the hybrid ASK/FSK WDM system configuration and b) the power spectral
density of a hybrid ASK/FSK modulated signal forPin=10dBm. The ASK and FSK
modulation rates are 10Gb/s and 1Gb/s respectively and the channel detuning is
=5GHz.
Fig. 5: System configuration of the pre-chirped optical WDM system.
Fig. 6: Eye diagrams for the central channel of a single span eight-channel WDM
system: a) conventional WDM system, b) application of the hybrid ASK/FSK
modulation and c) WDM with pre-chirped pulses. The transmission rate is 10Gb/s, the
channel spacing is 50GHz and the input power is 10dBm.
Fig. 7: Q factor of the central channel as a function of the input powerPin for a
10Gbps system of a) 8 channels and 50GHz channel spacing, b) 8 channels and
100GHz channel spacing, c) 16 channels and 50GHz channel spacing and d) 16
channels and 100GHz channel spacing
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Fig. 8:Q factor vs. input power for a single span eight-channel 40Gbps system
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